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Question
If tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to ______.
Options
1
2
3
4
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Solution
If tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to 3.
Explanation:
Given that: tanA = `1/2`, tanB = `1/3`
tan2A = `(2tan"A")/(1 - tan^2"A")`
= `(2 xx 1/2)/(1 - (1/2)^2`
= `1/(1 - 4)`
= `1/(3/4)`
= `4/3`
So, tan2A = `4/3` and tanB = `1/3`
tan(2A + B) = `(tan 2"A" + tan "B")/(1 - tan 2"A" . tan "B")`
= `(4/3 + 1/3)/(1 - 4/3 xx 1/3)`
= `(5/3)/((9 - 4)/9)`
= `5/3 xx 9/5`
= 3
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